The vibrational motions of a molecule in its equilibrium or during a chemical reaction provide a wealth of information about its structure, stability, and reactivity. This information is hidden in measured vibrational frequencies and intensities, however can be unraveled by utilizing quantum chemical tools and applying the Cal-X methods in form Vib-Cal-X. Vib-Cal-X uses the measured frequencies, complements them to a complete set of 3N-L values (N number of atoms; L number of translations and rotations), derives experimentally based force constants, and converts them into local mode stretching, bending, and torsional force constants associated with the internal coordinates describing the geometry of the molecule. This is done by utilizing the adiabatic vibrational mode concept, which is based on a decomposition of delocalized normal vibrational modes into adiabatic internal coordinate modes (AICoMs) needed to describe bonding or changes in bonding. AICoM force constants relate to the intrinsic bond dissociation energy (IBDE) of a bond and, accordingly, are excellent descriptors for bond order and bond strength. It is shown that bond dissociation energies, bond lengths, or bond densities are not directly related to the bond strength because they also depend on other quantities than just the bond strength: the bond dissociation energy on the stabilization energies of the fragments, the bond length on the compressibility limit distance between the atoms, the bond stretching frequency on the atom masses, etc. The bond stretching force constants however lead directly to bond order and bond strength as has been demonstrated for the bonds in typical organic molecules. Using this insight, the generalized vibrational frequencies of reacting molecules are used to obtain insight into the chemical processes of bond breaking and forming. An elementary chemical reaction based on these processes is characterized by a curved reaction path. Path curvature is a prerequisite for chemical change and directly related to the changes in the stretching force constants as they respond to the bond polarizing power of a reaction partner. The features of the path curvature can be used to partition the reaction path and by this the reaction mechanism in terms of reaction phases. A reaction phase is characterized by an elementary structural change of the reaction complex leading to a chemically meaningful transient structure that can convert into a real transition state or intermediate upon changing the environmental conditions or the electronic structure (substituents, etc.) of the reaction complex. A unified approach to the study of reaction mechanism (URVA: Unified Reaction Valley Approach) is discussed that is based extensively on the analysis of vibrational modes and that is aimed at detailed understanding of chemical reactions with the goal of controlling them.
Keywords: Cal-X methods, vibrational frequency, bond strength, chemical bond, adiabatic internal Coordinate mode (AICoM), unified reaction valley approach (URVA), reaction path curvature, reaction path, Reaction Mechanism, Vib-Cal-X, Quantum chemical tools, Vibrational Force Constants, Fermi resonance, Mossbauer spectroscopy, Overtone Spectroscopy, Bond Energy (BE), Bond Dissociation Energy (BDE), NMR Spin-Spin Coupling Constant, Reaction Path Hamiltonian, Electron Density Analysis, Analysis of Coriolis Couplings, Vibrational spectroscopy, Scalar curvature K(s), Diels-Alder reaction, Woodward-Hoffmann rules